Power allocation under per-antenna power constraints in multiuser MIMO systems

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1 33 0 Vol.33 No Journal on Councatons October 0 do:0.3969/.ssn x IO 009 IO IO N94 A X(0) Power allocaton under er-antenna ower constrants n ultuser IO systes HAN Sheng-qan, YANG Chen-yang (School of Electroncs and Inforaton Engneerng, Behang Unversty, Beng 009, Chna) Abstract: A low-colexty ower allocaton algorth was nvestgated under er-antenna ower constrants (PAPC) n ultuser ultle-nut ultle-outut (IO) systes. It was shown that the otal ower allocaton subect to PAPC, aed at axzng the su rate of ultle users wth zero forcng (Z) recoders, had the structure of water-fllng wth ultle water-levels. Based on ths result, the equvalence between PAPC and weghted su ower constrants was roved and a low-colexty subotal ower allocaton ethod was then roosed. Sulaton results show that the roosed ethod outerfors the exstng equal ower allocaton ethod and the heurstc ethod, and t can effcently reduce the coutatonal colexty wth a neglgble erforance loss coared wth the otal ower allocaton ethod. ey words: ultuser IO systes; er-antenna ower constrants; ower allocaton; zero forcng recoder U-IO, ultuser ultle-nut ultle-outut DPC [] DPC [] Z, zero forcng U-IO [3~5] [6] SPC, su ower constrants Z ZX oundaton Ites: he Natonal ey Proect of Next Generaton Wdeband Wreless Councaton Networs (0ZX ); Chna Postdoctoral Scence oundaton (004907)

2 7 33 DPC [7] PAPC, er-antenna ower constrantsz PAPC SPC [4, 5, 7, 8] PAPC [4,5] Z Z SPCwaterfllng[7] PAPC [9] [0] PAPC PAPC[] EPA, equal ower allocaton EPA EPA Z PAPC EPA ( ) ( ) H I dag( x) x IO Z g H h g 0 () h () Z Z R H γ h g () H h g log + log + (3) h g H H H G [ g, L, g ] P dag( ) [, L, ] W GP G g b g b (4) g, L, g PAPC Z a ax log +..,,, (5a) s t a L (5b) P 0,, L, b P P 3 (5)

3 0 IO 73 ( ) L( u; v) log + + u A v (6) u [ u, L, u ] v [ v, L, v ] A [ a, L, a ] a u v 0,, L, (7) u 0,, L, (8) v 0,, L, (9) ( ) u a 0,, L, (0) v 0,, L, () + ua v 0,, L, () + () u a v (3) (7)(9)()(3) ua + (4) u (8)(0) (5b) ( x) + ax( x,0) (4) u [] u u (4) u [] u ax log( + ) (5) s t wa.., 0 w [ w, L, w ] w w 0 (5) a, L, (5) w [ w, L, w ] a, L, () λ (6) λ wa wa (7) (5) [9] (5) (5) (4)(6) u λw (4) (6) u λw (8)(0) (5b) a, L, u λw (5b) λ > 0 0 w (8) w w (7) ( ) w A 0 (8) 0 w a (8) ( ) λw a 0,, L, (9) λ λ > 0 (9) u λw (0) u λw + w λ u w u / u w u

4 u (5) a w, L, (9) w w 0 w a w n ax q (0) w, L, q a (0) (0) w (5) w (5) w w (5) q 0 w w S [ s, L, s ] w w S w w µ w + ( µ ), s w µ w, s,,,, () 0 µ s w, w () 3 w w, w, w, s w, s + s q 0 q µ s s () µ s S ) µ n 0 µ ax ) µ ( µ n + µ ax ) / () w (6) ( w ) q ( w ) S 3) qs ax S q ( w ) µ ax µ µ n µ 4) ) 3) µ ax µ n ε < ε ) 0 S 0 φ 0 {, L, } w 0,, q ( ) w0 {, L, } ) + s arg ax q S S U{ s } {, S } () w µ qs µ µ 0 w w, w, 0 s s > µ q ( w ), L, q S ax q q ax q S 3) q > qs )(6) ( w ) ( w ) () ax a ax a ( w ) ( w ) 5 3 [0] []

5 0 IO 75 [9] P P / P / 5dB Z ε 0.0 ε 3 3(a) ε ε 0.0 3(b) (a) ε 4 8 ε GHz Pentu IV GB-RA ALAB ALAB tc/toc (b) 3 6 Z

6 76 33 q µ s qs 0 µ U U q µ s qs µ qs µ U U J, L, J U U U U µ π µ U (6) 0, π, π λ w, a (7) λ λ π w, a π + π π (3)(4) as + w, a π s as π π π w, a () w, a µ,, s B w, a (6)(5) as ( ( ( ) )) + µ B + µ as π s as π π ( ( ) ) µ B + µ as π as ( ( ( ) )) + µ B + µ as π as π π µ B + µ as π π π (3) (4) q (5) q w a µ w a + ( µ ) a (6) ( ( ) ) as ( ) ( ) + B B + as π π µ π π ( µ B + ( µ ) a ) s as E B µ (7) π ( µ B + ( µ ) a ) π s E + B + a π s π U q 0 0 µ s as E B 0 (8) π π ( µ B + ( µ ) a ) s q µ s q s (7) as ( ) as E B qs π π ( µ B + ( µ ) a ) (9) s a E B 0 B a E / s s as ( ) as E B π ( µ B + ( µ ) as ) as as E B µ as / ( ) ( ( ) ) E + µ as π µ B + µ as as E B µ E / + ( µ ) π ( µ B + ( µ ) a ) s (30) as 0 E B (30) q s as E B qs (3) µ E / + ( µ ) π ( µ B + ( µ ) a ) π s E > 0 > 0 0 µ µ E / + ( µ ) > 0 (8)(3) 0 q s qs U µ 0, L, J qs U w U λ ( w ) U U q µ s [] GESBER D, OUNOURIS, HEAH JR R, et al. Shftng the IO aradg: fro sngle user to ultuser councatons[j]. IEEE Sgnal Processng ag, 007, 4(5): [] DIIC G, SIDIROPOULOS N D. On downln beaforng wth greedy user selecton: erforance analyss and a sle new algorth[j]. IEEE rans Sgnal Processng, 005, 53(0): [3] WIESEL A, ELDAR Y C, SHAAI S. Zero-forcng recodng and generalzed nverses[j]. IEEE rans Sgnal Processng, 008, 56(9): [4] GESBER D, HANLY S, HUANG H, et al. ult-cell IO cooeratve networs: a new loo at nterference[j]. IEEE J Select Areas 85

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